Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Images of manifolds with semi-ample anti-canonical divisor


Authors: Caucher Birkar and Yifei Chen
Journal: J. Algebraic Geom. 25 (2016), 273-287
DOI: https://doi.org/10.1090/jag/662
Published electronically: August 27, 2015
MathSciNet review: 3466352
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Abstract | References | Additional Information

Abstract: We prove that if $ f\colon X\to Z$ is a smooth surjective morphism between projective manifolds and if $ -K_X$ is semi-ample, then $ -K_Z$ is also semi-ample. This was conjectured by Fujino and Gongyo. We list several counterexamples to show that this fails without the smoothness assumption on $ f$.

We prove the above result by proving some results concerning the moduli divisor of the canonical bundle formula associated to a klt-trivial fibration $ (X,B)\to Z$.


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Additional Information

Caucher Birkar
Affiliation: Department of Pure Mathematics and Mathematical Statistics (DPMMS), Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge, CB3 0WB, United Kingdom
Email: c.birkar@dpmms.cam.ac.uk

Yifei Chen
Affiliation: Hua Loo-Keng Key Laboratory of Mathematics, Institute of Mathematics, Chinese Academy of Sciences, No. 55 Zhonguancun East Road, Haidian District, Beijing, 100190, People’s Republic of China
Email: yifeichen@amss.ac.cn

DOI: https://doi.org/10.1090/jag/662
Received by editor(s): April 14, 2013
Received by editor(s) in revised form: February 24, 2014
Published electronically: August 27, 2015
Article copyright: © Copyright 2015 University Press, Inc.

American Mathematical Society